Of course, immediately after the time window over the past, another
observation
(of the near future) is also obtained from
the training data. One may again simply vectorize the parameters of
the perceptual system (the Gaussian tracking blobs) into yet another
vector (of dimensionality
). The
vector represents the past action and the
represents the
consequent reaction exactly at time t. For a few minutes of data, we
can obtain thousands of pairs of
and
vectors
(i.e. action-reaction pairs) by sliding the attentional window over
the time series (i.e. considering all values of t) and processing as
explained above. Figure 4.5 shows the evolution of the
dominant 3 dimensions of the
vectors as we consider an
involved interaction between two participants over time t of roughly
half a minute. This represents the evolution of the short term memory
of the learning system during half a minute.

Figure 4.5:
Eigenspace Properties
for

Given sufficient pairs of the vectors ((t),(t)) from
training data, it is possible to start seeing patterns between a short
term memory of the past interaction of two humans and the immediate
subsequent future reaction. A system which can forecast this behaviour
could predict what to do next and engage with a single human. However,
instead of learning an exact deterministic mapping between and ,
as is done in a predictive neural network, we will
discuss a more probabilistic approach. This involves estimating a
probability density denoted as
which yields the
probability of a reaction given a short history of past
action. We will always be observing the past ()
but the
future ()
is what we are trying to predict. We are not, for
instance, interested in the conditional pdf
,
which computes the probability of the past ()
given the
future. In other words, we will seldom use the learning system in the
almost `philosophical' task of describing the actions that could
have led to some future result, .
Mostly, we will query the
system about what future result should follow the actions it just
saw. The use of probabilistic techniques here allows the notion of
randomness and stochasticity which are more appropriate for
synthesizing compelling behaviour. In essence, they make the system
generate behaviour that is interesting and correlated with the past
and the user's stimulating actions but is also not entirely
predictable and contains some pseudo random choices in its space of
valid responses.